Question

find derivative of a function
f(x)=11-4x^3

Answer 1

Have you learned the `Power Rule for Derivatives` yet?
Or do you need to use the `Limit Definition of the Derivative` in order to solve this? :)

Answer 2

yes

Answer 3

yes to which? :) lol

Answer 4

power rule 4 derivatives

Answer 5

Ok cool c:

Answer 6

like x^3= 3x^2? is that d power rule?

Answer 7

yes good c:

Answer 8

hahha. im not sure.

Answer 9

\[\large f(x)=11-4x^3\]

See how the first term contains no variable? There is no variation, no change in 11. It is always constant.
The derivative measures the rate of change.
So how much does a constant change? Zero amount! It doesn't change, it's always 11 in this case.

That's a long-winded explanation of why the derivative of a constant is 0.

On the second term, we'll apply the power rule for derivatives (in this order):
~Bring the power down as a coefficient on the x.
~Decrease the power by 1.

Answer 10

\[\large -4x^3 \qquad \rightarrow \qquad -4\cdot3x^{3-2}\]Understand what we did there? We brought the 3 down as multiplication, and then we decrease the power by 1.

Answer 11

okay.. i got it. and then

Answer 12

-12x^2

Answer 13

\[\large f(x)=11-4x^3\]\[\large f'(x)=0-4\cdot3x^2\]We place a prime on the f, to show that we've taken it's derivative.

I see you have simplified it, good job! :)\[\large f'(x)=-12x^2\]

Answer 14

hold on. i have another one. it has square root

Answer 15

So this is what the problem looks like?
\[\large 2\sqrt x-\frac{3}{x^2}\]

Answer 16

yes

Answer 17

We can rewrite the square root term as a `Rational Expression`.
A Rational Expression is one which allows us to write the powers AND roots as exponents using fraction notation.\[\large \sqrt x=x^{1/2}\]The 2 in the denominator is to let us know that it's a 2nd root, or "square" root.

So that allows us to write our problem as,\[\large 2x^{1/2}-\frac{3}{x^2}\]

Answer 18

To deal with the second term, we'll have to remember some rules of exponents.
We can bring the x up to the numerator, by applying a negative to the power.\[\large 2x^{1/2}-3x^{-2}\]See how the 2 changed to a -2?

Answer 19

From here, everything is in a really nice format, so we can apply the `Power Rule` once again.

Answer 20

yes ;)